Abstract
Let Σ be a finite alphabet, and let h : Σ* → Σ* be a morphism. Finite and infinite fixed points of morphisms — i.e., those words w such that h(w) = w — play an important role in formal language theory. Head characterized the finite fixed points of h, and later, Head and Lando characterized the one-sided infinite fixed points of h. Our paper has two main results. First, we complete the characterization of fixed points of morphisms by describing all two-sided infinite fixed points of h, for both the “pointed” and “unpointed” cases. Second, we completely characterize the solutions to the equation h(xy) = yx in finite words.
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Research supported in part by a grant from NSERC. A full version of this paper can be found at http://math.uwaterloo.ca/~shallit/papers.html.
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Shallit, J., Wang, Mw. (1999). On two-sided infinite fixed points of morphisms. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_41
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DOI: https://doi.org/10.1007/3-540-48321-7_41
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